# A Geometric Approach to Free Boundary Problems (Graduate Studies in Mathematics No. 68 Illustrated edition)

By: Luis Caffarelli (author), Sandro Salsa (author)Hardback

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### Description

Free or moving boundary problems appear in many areas of analysis, geometry, and applied mathematics. A typical example is the evolving inter phase between a solid and liquid phase: if we know the initial configuration well enough, we should be able to reconstruct its evolution, in particular, the evolution of the inter phase. In this book, the authors present a series of ideas, methods, and techniques for treating the most basic issues of such a problem.In particular, they describe the very fundamental tools of geometry and real analysis that make this possible: properties of harmonic and caloric measures in Lipschitz domains, a relation between parallel surfaces and elliptic equations, monotonicity formulas and rigidity, etc. The tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems. This book is useful for supplementary reading or will be a fine independent study text. It is suitable for graduate students and researchers interested in partial differential equations. Also available from the AMS by Luis Caffarelli is ""Fully Nonlinear Elliptic Equations"", as Volume 43 in the AMS series, Colloquium Publications.

### Contents

Elliptic problems: An introductory problem Viscosity solutions and their asymptotic developments The regularity of the free boundary Lipschitz free boundaries are $C^{1,\gamma}$ Flat free boundaries are Lipschitz Existence theory Evolution problems: Parabolic free boundary problems Lipschitz free boundaries: Weak results Lipschitz free boundaries: Strong results Flat free boundaries are smooth Complementary chapters: Main tools: Boundary behavior of harmonic functions Monotonicity formulas and applications Boundary behavior of caloric functions Bibliography Index.

### Product Details

• publication date: 15/06/2005
• ISBN13: 9780821837849
• Format: Hardback
• Number Of Pages: 270
• ID: 9780821837849
• weight: 713
• ISBN10: 0821837842
• edition: Illustrated edition

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